LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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188 Ashish Gehani, Thomas LaBean, and John Reif Mathematical Society, 27, DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, 1995, 187–198. 48. E. Winfree, Simulations of Computing by Self-Assembly, Proceedings of the Fourth DIMACS Meeting on DNA Based Computing, 1998, 213–242. 49. E. Winfree, F. Liu, L.A. Wenzler, and N.C. Seeman, Design and Self-Assembly of Two Dimensional DNA Crystals, Nature, 394 (1998), 539–544. 50. E. Winfree, X. Yang, and N.C. Seeman, Universal Computation via Self-assembly of DNA: Some Theory and Experiments, DNA based computer II (Editors: L. Landwaber, E. Baum) DIMACS series in Discrete Math. and Theoretical Comp. Sci. 44 (1999) 191–214. 51. J. Ziv and A. Lempel, A universal algorithm for sequential data compression, IEEE Trans. Inf. Theory, IT-23 (1977), 337–343.
Splicing to the Limit Elizabeth Goode 1 and Dennis Pixton 2 1 Mathematics Department, Towson University Towson, MD 21252, USA egoode@towson.edu 2 Department of Mathematical Sciences, Binghamton University Binghamton, NY 13902-6000, USA dennis@math.binghamton.edu Abstract. We consider the result of a wet splicing procedure after the reaction has run to its completion, or limit, and we try to describe the molecules that will be present at this final stage. In language theoretic terms the splicing procedure is modeled as an H system, and the molecules that we want to consider correspond to a subset of the splicing language which we call the limit language. We give a number of examples, including one based on differential equations, and we propose a definition for the limit language. With this definition we prove that a language is regular if and only if it is the limit language of a reflexive and symmetric splicing system. 1 Introduction Tom Head [5] invented the notion of a splicing system in 1987 in an attempt to model certain biochemical reactions involving cutting and reconnecting strands of double-sided DNA. Since then there have been many developments and extensions of the basic theory, but some of the basic questions have remained unanswered. For example, there is still no simple characterization of the languages defined by splicing systems. The language defined by a splicing system is called the splicing language, and this corresponds to the set of molecular types that are created during the evolution of the system. In discussions several years ago Tom proposed analyzing the outcome of a splicing system in a way that is closer to what is actually observed in the laboratory. The idea is that certain molecules which appear during the biochemical reactions are transient in the sense that they are used up by the time the splicing experiment has “run to completion.” The molecules that are left at this stage can be termed the limit molecules of the system, and the corresponding formal language defined by the splicing system is called the limit language. The first major problem is to properly define this limit language. One possibility is to try to use differential equations to model the set of molecules, and then to define the limit language in terms of the solutions. Although it is reasonably clear how to set up such equations, solving them is another matter, since N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 189–201, 2004. c○ Springer-Verlag Berlin Heidelberg 2004
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Lecture Notes in Computer Science 2
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Nata˘sa Jonoska Gheorghe Păun Grz
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Thomas J. Head
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VIII Preface portant to keep in min
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X Table of Contents Formal Properti
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Solving Graph Problems by P Systems
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where Solving Graph Problems by P S
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Writing Information into DNA Masano
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Writing Information into DNA 25 Ham
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Writing Information into DNA 27 Fig
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Writing Information into DNA 29 Dea
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5 Results 5.1 DNA Code for the Engl
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Writing Information into DNA 33 3.
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Writing Information into DNA 35 101
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Balance Machines: Computing = Balan
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+ .. . + Balance Machines: Computin
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x Balance Machines: Computing = Bal
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1 Balance Machines: Computing = Bal
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Eilenberg P Systems with Symbol-Obj
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2 Definitions Definition 1. A strea
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5 Conclusions Eilenberg P Systems w
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Molecular Tiling and DNA Self-assem
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3 Molecular Self-assembly Processes
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8 Hierarchical Tiling Molecular Til
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References Molecular Tiling and DNA
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On Some Classes of Splicing Languag
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ˆxa ˆby ✬ ✩✬ ✩ a b x y
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The Power of Networks of Watson-Cri
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Fixed Point Approach to Commutation
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Here the last one holds if and only
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� � � � � Fixed Point App
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Remarks on Relativisations and DNA
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Remarks on Relativisations and DNA
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Page 163 and 164: Digital Information Encoding on DNA
Page 177 and 178: DNA-based Cryptography Ashish Gehan
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Page 201 and 202: Splicing to the Limit 191 molecular
Page 203 and 204: Splicing to the Limit 193 Discussio
Page 205 and 206: Example 9. The splicing rules are S
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Page 213 and 214: Formal Properties of Gene Assembly
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Transducers with Programmable Input
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Methods for Constructing Coded DNA
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u u Methods for Constructing Coded
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On the Universality of P Systems wi
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An Algorithm for Testing Structure
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Definition 1. Define the relation
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280 Manfred Kudlek Definition 5. Co
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On Languages of Cyclic Words 283 Th
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On Languages of Cyclic Words 285 No
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On Languages of Cyclic Words 287 Th
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A DNA Algorithm for the Hamiltonian
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Formal Languages Arising from Gene
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A Proof of Regularity for Finite Sp
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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The Duality of Patterning in Molecu
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The Duality of Patterning in Molecu
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Membrane Computing: Some Non-standa
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where: Membrane Computing: Some Non
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where: Membrane Computing: Some Non
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The P Versus NP Problem Through Cel
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Realizing Switching Functions Using
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Realizing Switching Functions Using
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AND Gate Realizing Switching Functi
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NOR Gate Realizing Switching Functi
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Plasmids to Solve #3SAT Rani Siromo
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Plasmids to Solve #3SAT 363 A comme
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Plasmids to Solve #3SAT 365 from th
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Communicating Distributed H Systems
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Proof Communicating Distributed H S
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Books: Publications by Thomas J. He
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Publications by Thomas J. Head 387
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Publications by Thomas J. Head 389
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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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